Level Spectra of OddEven 1f_{72}Shell Nuclei in the Coriolis Coupling Model
Abstract
The negative parity levels of oddeven nuclei with protons and neutrons in the 1f_{72} shell are calculated using the strongcoupling symmetricrotator model including the Coriolis coupling between bands. The singleparticle energy levels and wave functions in the deformed well are computed for a spinorbit strength C=0.26ℏω_{0} which is consistent with the observed splitting in Ca^{41}. The wellflattening parameter D is taken to be 0.06ℏω_{0} in the middle of the 1f_{72} shell and 0.035ℏω_{0} otherwise. The bandhead energies are calculated from the appropriate summation over the occupied singleparticle energy levels using ℏω_{0}=41A^{13} MeV for the energy of the oscillator quantum. The moment of inertia is taken from the excitation energy of the first excited 2^{+} state of neighboring eveneven nuclei assuming a rotational character for this state. The same value is used for all bands in any given nucleus. The matrix elements of the Coriolis coupling are computed from the singleparticle wave functions. The final excitation spectra are obtained by diagonalizing the Coriolis coupling term with the rotational wave function based on the ten available particle or core excited states in the 1f2p shell. Energy levels and wave functions are calculated as a function of the deformation parameter β the level spectrum for each individual nucleus is given for a tentative choice of β. The effect of a quenching of the Coriolis interaction on the calculated level spectrum is investigated. The computed level spectra for the nuclei (i) Sc^{43}, Sc^{45}, Sc^{47}, (ii) Ca^{43}, Ti^{45}, V^{47}, V^{49}, V^{51}, (iii) Ca^{45}, Ti^{47}, Cr^{49}, Mn^{51}, Mn^{53}, and (iv) Ti^{49}, Cr^{51} compare favorably with experiment. The model predicts the correct groundstate spin for all nuclei, including the anomalous cases of Ti^{47}, Cr^{49}, and Mn^{51} which have a 52^{} ground state. Thus the observed 72^{} (and occasionally 52^{}) groundstate configuration cannot be adduced as evidence supporting the validity of the sphericalshell model in the 1f_{72} shell. The positions of negative parity states with known spin especially the lowlying 32^{} statesare well accounted for in this model, in contrast with difficulties encountered in the shellmodel treatment. In particular, the model reproduces the observed groundstate triplets in V^{47} and in V^{49} and the lowlying 32^{} state in Cr^{51}. Further, this model predicts the correct number of levels below about 2.5MeV excitation energy for nuclei in the upper half of the 1f_{72} shell. For nuclei in the lower half of the 1f_{72} shell, more levels are observed than predicted, which suggests the presence of positive parity states arising from core excitation of the 2s1d shell. The natural classification of the 1f_{72} nuclei in this model according to their oddnucleon count is borne out by the similarity of the observed spectra. The natural shellmodel classification scheme in terms of the conjugate and equivalent pairs, on the other hand, does not seem to be supported by the experimental data.
 Publication:

Physical Review
 Pub Date:
 October 1966
 DOI:
 10.1103/PhysRev.150.919
 Bibcode:
 1966PhRv..150..919M